λC is tiny
The Compton wavelength h/(mec) ≈ 2.43 pm. Even big-angle scattering barely nudges visible light but meaningfully shifts X-rays.
Scale
Compton Scattering Calculator
Enter an incident photon wavelength and scattering angle to get the Compton shift Δλ, the final wavelength, and the photon energy change. Useful for X-ray labs, homework checks, and seeing how angle controls energy loss.
Results
Δλ (shift)
—
Positive = longer wavelength
Final wavelength λ′
—
Incident + Δλ
Energy before
—
Photon energy (keV/eV)
Energy after
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Lower for larger θ
Uses Δλ = (h / mec)(1 − cos θ) with me the electron rest mass.
Compton highlights
θ drives the loss
Δλ peaks at 180°. Forward scatter (θ≈0°) barely changes energy.
Geometry
Energy inverse to λ
E = hc/λ. A positive Δλ means lower photon energy and momentum—transferred to the electron.
Energy transfer
Quantum signature
Compton’s experiment showed light carries momentum like a particle, not just a wave—key evidence for photons.
History
Formula and assumptions
For a photon scattering off a free stationary electron, the wavelength shift is Δλ = (h / mec)(1 − cos θ). The term in parentheses is just geometry; the prefactor is the Compton wavelength λC. The final wavelength is λ′ = λ + Δλ and the energy follows from E = hc / λ.
This calculator assumes the initial electron is at rest and unbound. Bound electrons, relativistic electrons, or Klein–Nishina cross-section effects are out of scope here, but the simple formula is accurate for many X-ray setups and homework problems.